Dual Nature of Matter & Radiation

 

Dual Nature of Matter & Radiation :- 

Mutual interaction of radiation with substances such as Photoelectric effect(phenomenon in which electrically charged particles are released from or within a material when it absorbs electromagnetic radiation) Compton effect(Compton scattering occurs when a photon interacts with an outer orbital electron. In this interaction, the incident photon collides with an outer electron, which receives kinetic energy and recoils from the point of impact. The path of the incident photon is deflected by this interaction and is scattered in a new direction from the site of the collision. The energy of the scattered photon equals the energy of the incident photon minus the sum of the kinetic energy gained by the recoil electron and its binding energy) and Raman effect(The Raman Effect is the process of scattering of light particles by molecules of a medium. The scattering occurs due to a change in the wavelength of light as it enters the medium. When a beam of light travels through a dust-free, transparent chemical, a small fraction of the light emerges in directions other than where it should) could be achieved by Quantum theory of light(particle nature) while some other effects such as a reflection, refraction, interference, diffraction and polarization could be explained by wave nature of light. This is called the dual nature of light.

On the basis of symmetry de-Broglie hypothesized the association of waves with moving matter particles, which was later verified experimentally by Davission and Germer (Davisson-Germer experiment).

Electron Emission (Dual Nature of Matter & Radiation) :-

Metals have free electrons that are free from the bonds of their atoms but are bound in the boundary of the metal surface and generally do not come out of the metal surface because the attraction of ions keep them inside the metal. Some energy is required to eject these electrons from the metal surface.

Work function(Φ₀) :- The minimum amount of energy required to eject an electron from the metal surface is called it’s work function. It is usually represented by Φ₀ . The work function of a metal is fixed, while it is different for different metals.

The minimum energy(work function) that is required to emit an electron from the surface of a metal can be supplied to the free electrons by either of the methods given below :-

• Thermionic Emission :- Required thermal energy is provided to the free electrons by suitably heating it so as to enable them to come out of the metal.
• Field Emission :- Electrons are kept under the strong influence of the electric field to emit the electron out of the metal.
• Photo-electric Emission :- When the light of appropriate frequency is made to illuminate a metal surface, electrons are emitted from it. These photo-generated electrons are called Photoelectrons.
• Secondary Emission :- When high-energy electrons(primary electrons) hit the metal surface, they transfer their energy to the free electrons of the metal, so that the free electrons of the metal are emitted from the surface. These electrons are called secondary electrons and this phenomenon is called secondary emission.

Photoelectric Effect

(a) Hertz’s Observation

Hertz experiments on the generation and detection of electromagnetic waves in 1887 strongly established the wave nature of light. In his experiment of generating electromagnetic waves by sparking discharge, Hertz observed in 1887 that if ultraviolet light was incident at the cathode then the sparking becomes more rapid. Hertz could not explain this phenomena.

[Hertz experiment consists of two metallic plates of equal size, placed 60 cm apart, held parallel to each other. Two small spheres S₁ and S₂ are placed closed to each other and connected to the plates A and B by thick metallic rods respectively. Using an induction coil the spheres are charged to high value.

 

(b) Hallwach’s and Lenard’s Observations

Hallwach and Lenard studied photoelectric effect in detail during 1886 to 1902.

Lenard’s Observations :-

Lenard observed that if a potential difference is applied across the two metal plates enclosed in an evacuated tube no current flows in the circuit. When one plate(emitter plate) enclosed in the evacuated tube, kept at negative potential is exposed with ultraviolet radiations, current begins to flow. As soon as ultraviolet radiations falling on the emitter plate are stopped, the current flow is also stopped. These observations indicate that when ultraviolet radiations fall on a metal plate, electrons are ejected from it which are attracted towards the other metal plate kept at positive potential(collector plate).

The flow of electrons through the evacuated glass tube results in the current flow in the external circuit. Thus, light falling on the surface of emitter plate causes current in the external circuit. Hallwach and Lenard studied the variation of photoelectric current with collector plate potential and with frequency and intensity of incident light.

Hallwach’s Observations :-

Hallwach attached a negatively charged zinc plate to an electroscope and illuminated the plate with ultraviolet light then he found that the plate becomes neutral. When this neutral plate was illuminated with ultraviolet light, it was found that the plate becomes positively charged and the positive plate was further illuminated with ultraviolet light, the amount of positive charge increased on it. It is clear from the above observation that when ultraviolet light is incident on the metallic surface negatively charged particles are emitted from the metal surface.

With the discovery of electrons in 1897, it became certain that these negatively charged particles emitted due to light are electrons.

Definition of Photoelectric effect “When light of a suitable frequency (or more than this frequency) is incident on a metal surface, electrons are emitted from the surface of the metal. This phenomenon is called Photoelectric effect.”

Some related terms :-

• Work Function :- The minimum amount of energy that is required to eject an electron from a metal surface.
• Threshold Frequency :- The minimum frequency of light that can force an electron to emit from a metal surface.
• Threshold Wavelength: The maximum wavelength of light that can eject a photoelectron from the surface of a metal.

Experimental study of Photoelectric effect (Dual Nature of Matter)

The circuit given below is used to study the photoelectric effect :-

 

The apparatus consists of a vacuum tube (of quartz or glass) with light sensitive cathode C(called emitter) and anode A(called collector). The potential divider is connected between the cathode and anode to produce the desired potential difference. Voltmeter measures the potential difference between cathode and anode and the micro ammeter(μA) measure the small photoelectric current in the circuit. The commutator is connected to the circuit so that A and C can be kept at positive and negative potential or negative and positive potential.

Working :-

When light of suitable frequency falls on the cathode(C), then photo electrons are emitted from it. These emitted electrons accelerate towards the anode due to the applied potential difference and generate photoelectric current. This current is measured by micro ammeter.

The variation of photoelectric current can be studied with :-

1. Variation of intensity of incident light.
2. Variation of potential difference between cathode and anode &
3. Variation of frequency of incident light.

 

(1) Effect of variation of intensity of incident light on photoelectric current

To study the dependence of photoelectric current on intensity of incident light, we keep the frequency of the incident light and potential difference between cathode and anode constant and change the intensity of incident light.

Following graph is obtained between intensity of light and photoelectric current :-

With the increase in intensity of light the number of photons per second falling on the cathode increases. Which is clear from the above graph that the photoelectric current i.e. number of electrons emitted per second is directly proportional to the intensity of incident light.

So the photoelectric current is directly proportional to the intensity of incident light.

 

(2) Effect of potential difference between cathode and anode on photoelectric current

To study the dependence of photoelectric current on potential difference between cathode and anode, we keep the frequency and intensity of the incident light constant at a certain value.

Following graph is obtained between potential difference and photoelectric current :-

From the above graph we note that when the potential difference between cathode and anode is zero, some amount of photoelectric current flows in the circuit. This is because ejected electrons have their own kinetic energy. Now if we increase the potential difference the photoelectric current also increases and after some time it becomes saturated. The current becomes saturated because all the electrons emitted by the cathode reach to anode.

Now if we reverse the direction of potential difference by using reversing key and when this negative potential difference is increased, the value of photo current decreases and it becomes zero at a certain negative potential difference. It is called cutoff potential or stopping potential(V₀).

Stopping potential is the negative potential applied to the anode relative to the cathode at which the value of photoelectric current becomes zero.

Note :-

1. From above graph we note that for two different intensities of incident  light(I₁ & I₂), the stopping potential is same. Hence we can say that, the stopping potential does not depend on the intensity of light.
2. Stopping potential resist the flow of electrons from cathode do anode so we can say that stopping potential is actually a measure of the maximum kinetic energy of the electrons. Thus . Using this equation we can find the maximum kinetic energy () of the emitted electrons.
3. At stopping potential if we increase the intensity of incident light no photo current is observed. So maximum kinetic energy of photoelectrons does not depend on the intensity of light.

 

(3) Effect of frequency of incident radiation on photoelectric current

To study the dependence of photoelectric current on frequency of incident radiation, we take radiations of different frequencies but of same intensity.

For each radiation, we study the variation between photoelectric current and potential difference between the plates.

We find that initially for low values of frequency no current flows but at a value of frequency higher than a certain minimum value, the current starts to flow and with the increase in frequency the value of current also increases and after sometime the value of current becomes constant. This is called saturation current.

From the above graph we note that…

• The value of stopping potential is different for radiations of different frequency.
• The value of stopping potential is more negative for radiation of higher frequency.
• The value of saturation current depends on the intensity of incident radiation but is independent of the frequency of incident radiation.

 

The minimum value of frequency at which the emission of electrons starts from a metallic surface, is called threshold frequency(ν₀) and the maximum wavelength corresponding to threshold frequency is called threshold wavelength(λ₀). The values of threshold frequency and threshold wavelength are characteristics of a metal or substance and these are different for different substances.

Variation of stopping potential with the frequency of incident radiation

(Dual Nature of Matter)

If we plot a graph between stopping potential and the frequency of incident radiation for two different metals A and B we get the graph as shown below :-

From the above graph we note that :-

1. For a given material the stopping potential varies linearly with the frequency of incident radiation
2. For every material there is a certain minimum frequency called threshold frequency (ν₀) for which the stopping potential is zero.
3. More the work function for a given material,  greater is the value of threshold frequency.
4. We know that ⇒ . Rearranging the terms we get, . This is the equation of a straight line having intercept on potential axis = = .

So we can say the work function Φ₀ = e × magnitude of intercept on potential axis.

laws of photoelectric emission

(Dual Nature of Matter)

1. For a given photosensitive material and for a given value of frequency of incident radiation, the number of photoelectrons ejected per second is directly proportional to the intensity of incident light.
2. For every photosensitive material, there is a certain minimum value of frequency of incident radiation below which no emission of photoelectrons takes place. This frequency is called threshold frequency(ν₀).
3. Above the threshold frequency, the maximum kinetic energy of the emitted photoelectrons depends upon the frequency of the incident radiation and is independent of the intensity of the incident radiation.
4. If the frequency of incident radiation is equal to the threshold frequency then there is no time lag (10^-9 second or less) between the incidence of radiation and the emission of photoelectrons. So the photoelectric emission is an instantaneous process.

 

Next Topic :- Failure of wave theory to explain photoelectric effect